As a catalyst for purifying NOx contained in exhaust gas when fuel is burned under a lean air-fuel ratio, there is known a catalyst comprised of a carrier made of alumina on the surface of which a layer of a NOx absorbent comprised of an alkali metal or alkali earth is formed and on the surface of which a precious metal catalyst such as platinum is carried (for example, see Japanese Unexamined Patent Publication (Kokai) No. 6-108826). In this catalyst, when the catalyst is activated and the air-fuel ratio of the exhaust gas is lean, the NOx contained in the exhaust gas is stored in the NOx absorbent, while when the air-fuel ratio of the exhaust gas is made rich, the NOx which had been stored in the NOx absorbent is released and reduced.
However, this NOx absorption and release action is believed not to be performed when the catalyst is not activated. Therefore, in the internal combustion engine described in the above publication, when the catalyst is not activated, the catalyst is heated by an electric heater.